Expanded scaling relations for locomotion in sloped or cohesive granular beds

Abstract

© 2020 American Physical Society. Dynamic similarity, while commonly applied in fluid systems, has recently been extended to locomotion problems in granular media. The previous work was limited to locomotors in cohesionless, flat beds of grains under the assumption of a simple frictional fluid rheology. However, many natural circumstances involve beds that are sloped or composed of cohesive (e.g. damp or powdery) grains. Here we derive expanded scaling relations inclusive of these phenomena. To validate the proposed scalings, we perform discrete element method simulations with inclined beds and cohesive grains using rotating "wheels"of various shape families, sizes, and loading conditions in accord with the proposed scaling laws. The data show a good agreement between scaled tests, suggesting the usage of these scalings as a potential design tool for off-road vehicles and extraplanetary rovers and as an analysis tool for biolocomotion in soils.